What is the integral from 1 to b of 6cx^2-1 ?

The integral from 1 to b of 6cx^2-1 is 2cb^3-2c-b+1

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integral from 1 to b of 6cx^2-1

\int_{1}^{b} 6 c x^{2} - 1 d x

2 c b^{3} - 2 c - b + 1

Solution steps

\int_{1}^{b} 6 c x^{2} - 1 d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{b} 6 c x^{2} d x - \int_{1}^{b} 1 d x

\int_{1}^{b} 6 c x^{2} d x = 2 c (b^{3} - 1)

\int_{1}^{b} 1 d x = b - 1

= 2 c (b^{3} - 1) - (b - 1)

Simplify

2 c (b^{3} - 1) - (b - 1) : 2 c b^{3} - 2 c - b + 1

= 2 c b^{3} - 2 c - b + 1

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What is the integral from 1 to b of 6cx^2-1 ?
The integral from 1 to b of 6cx^2-1 is 2cb^3-2c-b+1